Name: friction on a banked road
Uploaded: 2026-06-24T13:03:27.731Z
Duration: 1 min 17 s
Channel: JoVE

Consider a bus of mass three megagrams having its center of mass at G moving along a banked road at a constant speed. The coefficient of static friction between the tires and the road is 0.5.
What is the maximum angle of the banked road where the bus would not slip or tip?
Drawing the free-body diagram, gravitational, frictional, and normal forces are denoted.
The frictional forces at two contacts are expressed, and the weight of the bus is resolved into its components.
Consider the condition for no slipping. Since the bus travels with constant speed, it satisfies the equilibrium conditions, and the resultant forces acting on it in both directions are zero.
Solving the two equations gives the maximum angle for no slipping.
When the bus starts tipping, it loses contact with the upper point, and no reaction or frictional force acts at the upper point.
To prevent tipping, the resultant moment about the lower point must be zero. Solving the equation gives the maximum angle for no tipping.

wrijving: probleemoplossing

Frictie is een essenti&#xEB;le kracht die de beweging van objecten in het dagelijks leven be&#xEF;nvloedt. Afhankelijk van de situatie kan het zowel gunstig als problematisch zijn. Neem bijvoorbeeld een bus met een massa van drie megagram en het zwaartepunt op een specifiek punt, die langs een hellende weg met constante snelheid beweegt. De statische wrijvingsco&#xEB;ffici&#xEB;nt tussen de banden en de weg is 0.5. Vind de maximale hoek van de hellende weg waarbij de bus niet zal slippen of kantelen.Allereerst moet er een visuele voorstelling worden gemaakt van de zwaartekracht-, wrijvings- en normaalkrachten die op de bus werken. Deze krachten zijn cruciaal om het evenwicht van de bus op de hellende weg te begrijpen.Vervolgens moeten de wrijvingskrachten bij de twee contactpunten tussen de banden en de weg worden geanalyseerd. Dit kan worden bereikt door rekening te houden met het gewicht van de bus en hoe dit interageert met de hoek van de hellende weg.<img style="height:350px;" src="/files/ftp_upload/14316/14316_PT_Figure_1v2.svg" alt="Figure 1" />Aangezien de bus met constante snelheid rijdt, voldoet deze aan de evenwichtsvoorwaarden. Dit betekent dat de krachten die in zowel verticale als horizontale richting op de bus werken in balans zijn, en de bus stabiel op de weg blijft.Door deze krachten en hun relaties te onderzoeken, kan men de maximale hoek vinden die ervoor zorgt dat de bus stabiel blijft zonder van de helling af te glijden.<img style="height:13px;" src="/files/ftp_upload/14316/14316_PT_Equation_1v2.svg" alt="Equation 1" /><img style="height:13px;" src="/files/ftp_upload/14316/14316_PT_Equation_2v2.svg" alt="Equation 2" />Nu moet de kantel conditie worden onderzocht. Wanneer de bus begint te kantelen, verliest deze contact met het bovenste punt (het contactpunt tussen de bovenste band en de weg) en is er geen reactie- of wrijvingskracht op het bovenste punt.<img style="height:13px;" src="/files/ftp_upload/14316/14316_PT_Equation_3v2.svg" alt="Equation 3" /><img style="height:13px;" src="/files/ftp_upload/14316/14316_PT_Equation_4v2.svg" alt="Equation 4" />Om kantelen te voorkomen, moeten de krachten die op de bus werken in evenwicht zijn op zo&#x27;n manier dat het resulterende moment rond het onderste punt nul moet zijn. Dit helpt bepalen wat de maximale hoek is voor geen kantelen, ervoor zorgend dat de bus stabiel blijft zonder om te vallen.

Wrijving: Probleemoplossing

Friction is an essential force that influences the motion of objects in daily life. Depending on the situation, it can be either beneficial or ...

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Education

JoVE Core

Mechanical Engineering

Werktuigbouwkunde

Unit 1

Friction

Wrijving

KEY TERMS AND CONCEPTS

BELANGRIJKE TERMEN EN CONCEPTEN

Friction: Problem Solving

friction on a banked road

Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip.

To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road, and static friction is the grip that prevents sliding. The bus is then analyzed at the two tire contact points so the force balance can be checked.

Because the bus moves at a constant speed, it is in equilibrium. That means the vertical and horizontal forces cancel each other. Using the bus weight and the road angle, the maximum angle for no sliding can be determined from these balanced forces.

The tipping condition must also be checked. When tipping starts, the bus loses contact at the upper tire contact point. At that point, no reaction force or frictional force acts there. To avoid toppling, the moment about the lower contact point must be zero. That balance gives the largest safe bank angle without tipping.

Friction on a Banked Road

dry friction

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characteristics of dry friction

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types of friction problems

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friction: problem solving

Friction on a banked road affects whether a bus stays steady while it moves at constant speed. In this problem, a bus with a mass of three megagrams travels on a sloped road. The coefficient of static friction between the tires and the road is 0.5. The goal is to find the maximum bank angle where the bus will not slip or tip. To solve the motion part, the forces on the bus must be shown first. These include gravity, the normal force, and friction. The normal force is the push from the road,...

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collar bearings

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journal bearings

Friction Moment in Journal Bearings

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bearings: problem solving

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key terms and concepts

Find the maximum bank angle for a bus on a banked road by balancing gravity, normal force, static friction, and tipping moments.

Friction on a Banked Road | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Friction on a Banked Road

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